Cardinalities of Infinite Sets: Proving Bijective Relationship (0,1) and (0,2)

[knowLittle]

Homework Statement

Explain why $(0,1 )$ and $(0,2)$

I have proved that a function $f: (0,1 ) -> (0,2)$defined by f(x) =2x is bijective.

Homework Equations

The Attempt at a Solution

I could state that due to the sets relationship being bijective they have the same cardinality, but this is only true if both sets are finite. Here, (0,1) and (0,2 ) are infinite.

Any help?

 

[micromass]

What is your definition of "having the same cardinality"?

 

[knowLittle]

Nevermind, you are right. The definition of same cardinality or numerically equivalency doesn't restrict finite from infinite sets.

 

[micromass]

Nevermind, you are right. The definition of same cardinality or numerically equivalency doesn't restrict finite from infinite sets.

Right! So you solved the problem correctly. Congratz!